Decomposition Pipeline for Large-Scale Portfolio Optimization with Applications to Near-Term Quantum Computing

TL;DR

This paper introduces a decomposition pipeline for large-scale portfolio optimization that reduces problem size significantly, enabling the use of near-term quantum computers for practical solutions.

Contribution

The paper presents a novel decomposition pipeline combining correlation matrix preprocessing, spectral clustering, and risk rebalancing for portfolio optimization.

Findings

Reduces problem size by approximately 80%.

Drastically decreases computation time for solvers.

Enables the use of near-term quantum devices for optimization.

Abstract

Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman's algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization.